Abstract
Let (V, 0) be an isolated hypersurface singularity defined by the holomorphic function \(f: (\mathbb {C}^{n}, 0)\rightarrow (\mathbb {C}, 0)\). The k-th Yau algebra Lk(V ) is defined to be the Lie algebra of derivations of the k-th moduli algebra \(A^{k}(V) := \mathcal {O}_{n}/(f, m^{k}J(f))\), where k ≥ 0, m is the maximal ideal of \(\mathcal {O}_{n}\). The Generalized Cartan matrix Ck(V ) is an object associated to Lk(V ). We previously proposed a conjecture that ADE singularities can be completely characterized by Ck(V ), and verified it for k = 1 in our previous work. In this paper, we continue this work and verify this conjecture for k = 2.
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Presented by: Peter Littelmann
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Both Yau and Zuo are supported by NSFC Grants 11961141005. Zuo is supported by NSFC Grant 11771231. Yau is supported by Tsinghua University start-up fund and Tsinghua University Education Foundation fund (042202008). Naveed is spported by innovation team project of Humanities and Social Sciences in Colleges and universities of Guangdong Province (No.: 2020wcxtd008).
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Hussain, N., Yau, S.ST. & Zuo, H. Generalized Cartan Matrices Associated to k-th Yau Algebras of Singularities and Characterization Theorem. Algebr Represent Theor 25, 1461–1492 (2022). https://doi.org/10.1007/s10468-021-10074-6
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DOI: https://doi.org/10.1007/s10468-021-10074-6